Which of the following is an example of $\mathrm{negative} \mathrm{acceleration}$?

• A. A car moving forward and slowing down
• B. A cyclist moving at $\mathrm{constant} \mathrm{speed}$
• C. A train moving backward and increasing its $\mathrm{speed}$
• D. A ball rolling down a hill and speeding up

Answer: (A)

Verified step by step guidance

1. Understand that acceleration is the rate of change of velocity with respect to time, and it is a vector quantity, meaning it has both magnitude and direction.
2. Recognize that negative acceleration, often called deceleration, occurs when an object slows down in the direction of its motion. This means the acceleration vector is opposite to the velocity vector.
3. Analyze each option by considering the direction of velocity and whether the speed is increasing or decreasing:
4. - A car moving forward and slowing down: velocity is forward, speed decreases, so acceleration is opposite to velocity (negative acceleration).
5. - A cyclist moving at constant speed: speed does not change, so acceleration is zero.
6. - A train moving backward and increasing speed: velocity is backward, speed increases, so acceleration is in the same direction as velocity (positive acceleration).
7. - A ball rolling down a hill and speeding up: velocity and acceleration are in the same direction (positive acceleration).